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100 mg mass of nichrome metal is drawn i...

100 mg mass of nichrome metal is drawn into a wire of area of cross-section 0.05 mm. Calculate the resistance of this wire. Given density of nichrome` 8.4 xx 10^3 "kgm"^(-3)` and resistivity of the material as `1.2 xx 10^(-6) Omega` m.

Text Solution

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`m = 100mg = 100 times 10^(-6) kg`
`A = 0.05 mm^(2) = 0.05 times 10^(-6) m^(2)`
Density, `D = 8.4 times 10^(3) kgm^(-3)`
`p = 1.2 times 10^(-6) Omega m`
`D = (mass)/ (volume) = (m)/(AI)`
`I= (m)/(D times A)`
Resistance, `R = p(1)/(A)`
`R = p((m)/(D times A)) (1)/(A) = 1.2 times 10^(-6) times (100 times 10^(-6))/(8.4 times 10^(3) times 0.05 times 10^(-6)) times (1)/(0.05 times 10^(-6)) = 5.72 Omega`
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